Authorities have failed to swiftly remove killer trees from Central Park, claims the family of a man crushed to death in February by a falling limb.

A decayed American elm was marked as dangerous weeks before one of its snow-laden branches fell on the head of Elmaz Qyra, 46, an Albanian immigrant and married father of two walking through the park Feb. 25 after finishing his busboy shift at the New York Athletic Club, a lawsuit alleges.

The high-powered Conservancy, which controls most of the maintenance for the city’s most famous green space, again marked the tree near East 67th Street for removal on Jan. 13. But it never followed through, court papers claim.

A month later, the Brooklyn dad was fatally struck.

It was the second time in less than a year that someone was badly hurt by a falling Central Park tree limb. In July 2009, Google engineer Sasha Blair-Goldensohn was left with brain and spinal cord damage when a four-inch thick branch near West 64th Street fell on him.

None of the tree branches lining the iconic Literary Walk, where statues of Shakespeare, Walter Scott and Columbus stand, was pruned or removed in the two months prior to Qyra’s death, according to the Brooklyn Supreme Court lawsuit, which seeks unspecified damages.

“If the tree had been removed, my client would still be alive,” said lawyer Alan Shapey.

“I think they [the Conservancy] have a lot of explaining to do.”

Neither the Parks Department nor the Conservancy would comment on the pending litigation.